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  • Articles: DFG German National Licenses  (192)
  • 1975-1979  (192)
  • 1977  (192)
  • Computational Chemistry and Molecular Modeling  (192)
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  • Articles: DFG German National Licenses  (192)
Material
Years
  • 1975-1979  (192)
Year
  • 1
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 11 (1977), S. 59-71 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The goodness of the local fit of an approximate wave-function, \documentclass{article}\pagestyle{empty}\begin{document}$ \tilde \psi $\end{document}, to the exact function, ψ0, is \documentclass{article}\pagestyle{empty}\begin{document}$ |\tilde \psi - \psi _0 | $\end{document}. From this quantity the global accuracy of \documentclass{article}\pagestyle{empty}\begin{document}$ \tilde \psi $\end{document} is defined and a “working supposition” is presented, which quantitatively relates the global accuracy to the accuracy of expectation values. Two criteria based on the accuracy of the reduced local energy and the density respectively, are presented as alternatives to \documentclass{article}\pagestyle{empty}\begin{document}$ |\tilde \psi - \psi _0 | $\end{document}. The relative global accuracies of eight wave-functions for H2 are determined using the two criteria. The ‘working supposition’ is applied and predictions are made concerning the relative accuracies of the expectation values of the following operators: z2, r2, x2 + y2, 3z2 -; r2, ξ, rA-1, r12-1, and EL (the reduced local energy). The success rate is high (〉90%) except for those operators which are sensitive to interelectron coordinates or derivatives of the wave-function.
    Additional Material: 4 Tab.
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  • 2
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 11 (1977), S. 907-916 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 11 (1977), S. 1001-1004 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Type of Medium: Electronic Resource
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  • 4
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 11 (1977), S. 49-57 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The helix-coil phase transition of DNA is studied through a model equivalent to the one used in the theory of superconductivity. A distribution function for the excitations analogous to the usual Fermi function is obtained which depends on the parameter T0, the maximum temperature at which all pairs of bases are bonded. The expression for the number of unbonded pairs of bases depends only on the two parameters, T0 and Tc (critical temperature).
    Additional Material: 4 Ill.
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  • 5
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 11 (1977), S. 103-127 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Quantum mechanical tunneling theory is applied to the problem of synaptic vesicle release and to the problem of electric transmission at the ephaptic junction. In the synapse the tunneling produces conformational changes in macromolecules to open and close vesicle macrogates. Quantum mechanical tunneling as a basis for charge transfer and physical release of vesicles at junction membranes provides a unified concept of ephaptic and synaptic transmission. Details of this model are in agreement with experimental data for miniature endplate potential frequency and delay effects as a function of polarization, osmotic pressure, and temperature. The theory accounts for anatomical specializations at the synaptic cleft and the narrow junction observed for the ephapse.
    Additional Material: 5 Ill.
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  • 6
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 11 (1977), S. 187-187 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Type of Medium: Electronic Resource
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  • 7
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 11 (1977), S. 185-185 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Type of Medium: Electronic Resource
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  • 8
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 12 (1977), S. 115-131 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Three simplifying methodds are discussed and applied to the four lowest valence states of CH2(3B1, 1A1, 1B1 and 1Σg+(1A1*)) and to the two lowest of CH2+(2A1 and 2∏u(2B1)). These methods concern: (1) the development of polarization functions for Gaussian-lobe basis sets by least-square fitting of numebrical multiconfigurational atomic fuinctions (this approach is tested also on (C2H2, (2) the use of intermediate Hamiltonians to calculate avoided crossings between potential hypersurfaces, and (3) thecalculation of correlation energies using an atoms-in-molecule approach.The calculated equilibrium geometries of the CH2 States are within 0.02 Å and 5° of available experimental data. The calculated term values and ionization potentials, Te(1A1 = 0.35 eV, Te (1B1) = 1.22 eV, Te (1Σg+(1A1*)) 2.48 eV, I.P. (2A1) = 10.39 eV and I. P. (2∏u(2B1)) = 10.58 eV, are in agreement with some recent theoretical studies, and are very close to existing experimental information.
    Additional Material: 1 Ill.
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  • 9
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 12 (1977), S. 193-205 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The focal point of our discussion is the examination of truncated basis sets used in obtaining an accurate first principles clculation of the effective valence shell Hamiltonian by the canonical transformation-cluster expansion approasch. Subsequent diagonalization of this effecitve valence shell hamiltonian yields the valence shell transition energies. A detailed analysis of numerical results obtained using a number of different basis sets of hydrogen-like orbitals together with rigorous symmetry arguments celarly demonstrates the special role played by d orbitals in computing the 3P → 1D transition energy in carbon. The failure of early attempts to calculate the effective Hamiltonian for ethylene from first principles is examined in the light of recent ab initio calculations on ethylene involving d orbitals and the computations reported in this paper. We conclude that accurate calculations of the effective valence shell Hamiltonian for molecules must consider d orbitals in the excited orbital basis set.
    Additional Material: 1 Ill.
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  • 10
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 11 (1977), S. 543-559 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Quasi-relativistic (QR) versions of the CNDO and Mulliken-Wolfsberg-Helmholz (MWH) semiempirical methods based on the SCF-QR-MO-LCAO method given earlier are worked out. For the CNDO method only the basic formulas and matrix element expressions are given, while for the MWH one, the parametrization as well as the basis functions and group spinor overlap integral calculation were discussed. (PtCl6)2- complex was chosen for a test calculation. The energy level values and LCAO coefficients were obtained and compared with the nonrelativistic calculations. One of the results was the occurrence of a very strong reduction of the spin-orbit interaction due to covalency. The calculation proves the semi-empirical versions of the QR-MO-LCAO method to be quite realizable in practice.
    Additional Material: 3 Ill.
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  • 11
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 11 (1977), S. 715-723 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: We report in this work SCF atomic calculations for Li, Be, B, C, and Ne using a basis set of completely loge-localized functions. For these second row atoms the total volume R3 was partitioned into a spherical loge of radius R and its volume complement. The loge-localized basis functions were constructed as a product of Slater-type orbitals and a cut-off factor. The energy values obtained differ significantly from the Hartree-Fock ones indicating that the delocalization effects - not included in these calculations - are important.
    Additional Material: 6 Tab.
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  • 12
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 11 (1977), S. 767-773 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Gaussian orbital LCAO MO calculations are reported for pyrazine in its ground and first excited triplet state, together with calculations on its anion and cation. Energies, population analysis indices, and one-electron properties are compared across the series in order to investigate the differences in electron distribution.
    Additional Material: 5 Tab.
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  • 13
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 12 (1977), S. 759-763 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The spherical limit of a single particle in the field of three nuclei is shown to exhibit a variety of phenomena associated with the stability of the various extrema involved. Some consequences with respect to the general problem of detecting broken symmetry solutions of variational problems are pointed out.
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  • 14
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 12 (1977), S. 737-757 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Many-body perturbation calculations have been performed for the ground state of the carbon monoxide molecule at its equilibrium internuclear separation. The calculations are complete through third order within the algebraic approximation; i.e., the state functions are parameterized by expansion in a finite basis set. All two-, three-, and four-body terms are rigorously determined, and many-body effects are found to be very important. A detailed comparison is made with a previously reported configuration interaction study. Padé approximants to the energy expansion are constructed. The many-body perturbative wave function is used in the Rayleigh quotient to produce upper bounds to the electronic energy.
    Additional Material: 4 Ill.
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  • 15
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 12 (1977), S. 765-776 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The effect of damping factors on convergence to general stationary solutions in many-shell SCF theory is discussed using a first order perturbation analysis. Their bearing on the maximum overlap criterion is examined and a comparison made with Hartree damping. Examples are drawn from numerical experience with hole state and transition operator calculations, some of which lead to saddle point stationary conditions. The method of Hsu et al. is reviewed in the light of the foregoing arguments.
    Additional Material: 1 Tab.
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  • 16
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 12 (1977), S. 777-779 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
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  • 17
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 12 (1977), S. 805-811 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The PCILO method was used to study systems with the following types of intermolecular hydrogen bonds, involving 2nd row atoms: N…H—S, S…H—S, N…H—Cl, Cl…H—F, Cl…H—Cl, P…H—N, P…H—P, P…H—F, S…H—F.In all the cases calculated, the PCILO method yields an accurate qualitative description of the stabilization energies and to some extent quantitatively good agreement with reliable ab initio and experimental results. The corresponding equilibrium distances are in almost all cases smaller (up to 0.6 Å) than the ab initio values of the same compounds.
    Additional Material: 2 Ill.
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  • 18
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 12 (1977), S. 841-850 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The PCILO method was used to study systematically systems with the following types of intermolecular hydrogen bonds: . In all cases the PCILO method gives a correct description of the stabilization energies in a good agreement with reliable ab initio results. The PCILO calculated equilibrium distances are only somewhat smaller than the corresponding experimental or ab initio values. Qualitatively, also, the changes in the charge distributions are in accordance with the results of ab initio calculations.
    Additional Material: 3 Ill.
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  • 19
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 12 (1977), S. 105-113 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Momentum densities obtained from the Heitler-London (HL) wave functions for diatomic molecules and those from the corresponding valence-bond (VB) wave functions including ionic terms are compared. In each case they shown maxima in the direction perpendicular to the bond. However, the dependence of momentum densities on mutual orientations of the two electronic momenta is quite complex in the latter case. The improvement in the Compton profile on including the ionic terms is illustrated with the example of H2. The momentum denmsities obtained from the VB wave function constructed from orthogonalized atomic orbitals (OAO) have also been examined. The HL wave function with OAOS leads to the same momentum distribution as the repulsive state HL wave function constructed from overlapping AOS.
    Additional Material: 1 Tab.
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  • 20
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    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 11 (1977), S. 393-398 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The relations between the Waller-Hartree spin-free method and the symmetric group theory are given. It is shown that the Gallup method is a special case of ours with S = M. Furthermore, all the irreducible representation matrices and other matrices needed are written explicitly in terms of Sanibel coefficients which makes the method more useful. However, it was shown that the cases with S ≠ M for the spin-free pure spin states might be beyond the power of the symmetric group theory.
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  • 21
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    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 11 (1977), S. 381-391 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: A quantum calculation of the optical activity and gyrotropic birefringence is used in a molecular crystal to deduce symmetry properties. A study of the variation of the components of these tensors, when a change of origin occurs, is used to account for the formula for the electric excitation proposed by Landau and Lifchitz. It is shown that the results obtained are valid in the case of crystals with nonlocalized electrons.
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  • 22
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 12 (1977), S. 495-503 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: An exact collision theory of unimolecular and bimolecular gas phase reactions is derived from a general quantum-mechanical formulation of reactions rates based on the assumption that the reactants are in thermal equilibrium. In this way the quantum corrections to the classical collision theory expressions are rigorously defined. Approximate formulas for these corrections make it possible to determine well the temperature ranges within which the classical and the semiclassical approximations are valid. A comparison is made between the collision and the transition state theory with emphasis on some conceptual difficulties of the latter in treating the simple decomposition and recombination reactions. It is shown that in the classical (high temperature) limit these theories are incompatible except when the reaction coordinate is entirely separable (i.e., when the transition state theory is no longer useful).
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  • 23
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Further developments of a recent semiempirical, variable effective charge MO theory for calculation of ionization potentials (IP) and electron affinities (EA) as energy differences between separately minimized ground and ionized states are reported. The method is extended to adiabatic as well as vertical IPS and EAS by including core repulsion and σ bond compression energies in the total energy. The method is generalized to heteroatomic systems and is simplified by neglecting penetration integrals. As before, only two molecular parameters, the vertical IPS of benzene and naphthalene, are required to set the magnitude of the σ changes associated with the polarization of the core during loss or gain of a π charge. Twenty-seven aromatic molecules are studied, including polyacenes, condensed ring compounds, nonbenzenoids with five and seven member rings, nonplanar molecules, and heteroatomics with N+, as in pyridine, N+2, as in pyrrole, and O+2, as in furan. The results are within 0.2 eV of the photoelectron spectroscopic vertical IPS and the predicted vertical-adiabatic separation is consistent with the shape of the first band. The calculated EAS are within 0.2 eV of the observed values.The calculation is used to predict the IP and EA of the ionic photosensitizing cyanine dye, pinacyanol. The values obtained are consistent with the latest measured IP and EA of the adsorbed dye, corrected for surface and aggregation polarization effects.
    Additional Material: 3 Ill.
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  • 24
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: A condition for the equivalence of the Löwdin orthogonalization method and various localization methods is derived, taking the matrix elements of the localizing operator into consideration. In the example of the π atomic orbitals of benzene, it is shown that the “ultralocalized” functions defined in the Anderson fashion with help of the Boys minimum-fluctuation criterion do not fulfill this condition, in contrast with a Ruedenberg-type localization.
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  • 25
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 12 (1977) 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
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  • 26
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    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 12 (1977), S. 671-681 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: A method recently developed for the calculation of intramolecular nonbonded interactions based on experimental bond polarisabilities and atomic charges and transition π-charges obtained from MO calculations has been applied to the alanyl dipeptide. The potential energy contours in the φ, ψ plane obtained by this method compare favourably with those derived from the frequency of occurrence of conformations in globular proteins. An analysis of the various components of the nonbonded interaction energy indicates that the fairly frequent occurrence of conformations around φ = -80°, ψ=0° is presumably due to a favourable interaction of the π-polarisation.
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  • 27
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    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 12 (1977), S. 549-559 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Energy-shifted perturbation theory is studied in connection with corrections to Koopmans' theorem. The first three vertical Ionization potentials of N2, C2H2, and HCN are computed with basis sets of double-zeta Gaussian-type orbitals and double-zeta GTO plus polarization functions. The average absolute deviation of calculation ionization potentials from the observed values is found to be 0.4 eV, whether one uses Brillouin-Wigner or Rayleigh-Schrödinger perturbation theory.
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  • 28
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    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 12 (1977), S. 591-591 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
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  • 29
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    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 12 (1977), S. 609-622 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Diagrammatic many-body perturbation theory is used to calculate the potential energy function for the X1 σ+ state of the CO molecule near the equilibrium nuclear configuration. Spectroscopic constants are derived from a number of curves which are obtained from calculations taken through third order in the energy. By forming [2/1] Padé approximants to the constants we obtain: re = 1.125 Å (1.128 Å), Be = 1.943 cm-1 (1.9312 cm-1), aBe = 0.0156 cm-1 (0.0175 cm-1), We = 2247 cm-1 (2170 cm-1), WeXe = 12.16 cm-1 (13.29 cm-1), where the experimental values are given in parenthesis.
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  • 30
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    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 12 (1977), S. 623-637 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Functions of several variables, such as the electron density and the nuclear Born-Oppenheimer potential, may be analysed very effectively using orthogonal trajectories. In particular the behaviour of these trajectories at critical points of the functions is investigated in detail. The use of orthogonal trajectories in the virial partitioning of Bader and in the definition of reaction coordinates is extended. A chemical interpretation of the critical points is suggested. The relevance of catastrophe theory is illustrated.
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  • 31
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    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 12 (1977), S. 683-705 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Approximate numerical linear dependence among the columns of the two-electron integral matrix and the positiveness of the Coulomb operator are exploited in order to reduce the number of integrals that need to be calculated when a numerical accuracy is given by the machine in use or by the choice of the investigator. Numerical results presented indicate that the method leads to an algorithm for carrying out the two-electron integral four-index transformation which in practice can be achieved in a small fraction (˜1/5-1/3) of the time required to generate the integrals by one of the fastest available Gaussian integral programs, Almlöf's MOLECULE. This effectively removes one of the major bottlenecks of computational quantum chemistry.
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  • 32
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    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 12 (1977), S. 721-735 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: A new derivation of the Born-Oppenheimer separation of electronic and nuclear motion is presented. The arguments used differ from those in earlier works in not being specially designed for molecules. Instead they aim at an intuitive understanding of the qualitative behavior of the low energy bound states of any, real or hypothetical, Coulomb interacting system of particles. The virial theorem is the starting point of the discussion. After a brief explanation of how it can be used to understand atomic structure it is applied to molecules. It is found that coordinates of collective and individual motion are natural coordinates for the approximate separation, rather than nuclear and electronic. It is also shown that it is the form of the interaction between the particles that is responsible for the separation; the smallness of met/MNu is irrelevant.
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  • 33
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    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 12 (1977), S. 781-783 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
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  • 34
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    International Journal of Quantum Chemistry 12 (1977), S. 785-794 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Specific properties of systems with dipole-dipole interactions in the one-dimensional structures leading to the violation of the statistical equivalent of the continuity equation resulting in the creation of qualitatively new excitations are analyzed. Those excitations are the result of the interaction between the initial quasiparticle currents. The structures discussed may be of importance in biophysics, and the biophysical aspects of the obtained results are considered. In comparison with other mechanisms, the exciton mechanism is shown to be of a very specific nature as its transport properties are sharply dependent upon the type of exciting light bounded within the range of temperatures covered by living organisms. This can result in an accumulation of interface excitations on a specific lattice molecule and cause its qualitative transformations with corresponding biological consequences.
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  • 35
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    International Journal of Quantum Chemistry 12 (1977), S. 851-858 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Stabilization energies and equilibrium distances of one-dimensional (HF)n and (H2O)n chains have been calculated by means of the PCILO method for finite chain length and by the PCILOCC method for infinite chain length. Both types of calculation are compared with corresponding CNDO/2-MO and CNDO/2-CO calculations. Further we have performed an analysis of the individual contributions of the stabilization energies per monomer of the PCILO and PCILOCC calculations.The results show that the PCILOCC method is well suited for the calculation of molecular associations with translational symmetry.
    Additional Material: 1 Ill.
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  • 36
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    International Journal of Quantum Chemistry 12 (1977), S. 915-923 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: MO calculations of electronic structure and optical transitions for [VOn]5 -; 2n (n = 4, 5, 6) clusters in V2O5 monocrystals have been carried out by means of the semiempirical CNDO CI method. Using the calculated results, a complete analysis of V2O5 optical data as available in the literature and as obtained in the electroreflectivity experiments presented in this paper is performed. An identification of optical transitions in a wide energy range is presented. The optical properties of vanadium pentoxide are shown to be due to the localized charge transfer electronic transitions in the clusters. The fine structure of optical spectra is connected with the covalent splittings of the vanadium 3d and oxygen 2p atomic levels.
    Additional Material: 4 Ill.
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  • 37
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    International Journal of Quantum Chemistry 12 (1977), S. 925-935 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: We have reduced the Breit-type equation written down for 3 electrons to the 8 large components of the wave function in the (v/c)2 (Pauli) approximation. This procedure required appropriate handling of the 64 scalar equations which result in this instance. According to the results obtained within the accuracy of (v/c)2 all the terms are the same as those obtained by summing up the terms of the reduced 2-electron Breit's equation to 3 electrons. This statement is no longer valid, however, if during the reduction procedure we would go beyond the (v/c)2 approximation. Finally there is a discussion about how to begin developing a relativistic many-electron theory valid for the inner shell electrons of heavy atoms within the accuracy of the fine structure constant.
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  • 38
    Electronic Resource
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    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 12 (1977) 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
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  • 39
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Reference completely ab initio 6-3G and nonempirical 3G/MODPOT (ab initio effective core model potential) LCAO-MO-SCF calculations (using the same valence atomic orbital basis) were performed for a series of boron hydrides (B4H10, B5H9, B5H11, and B6H10) and a test 3G/MODPOT + VRDDO (variable retention of diatomic differential overlap for charge conserving integral prescreening) calculation were also performed for B5H9, B6H10, and B10H14. The agreement between the ab initio 6-3G and the corresponding 3G/MODPOT calculations was excellent for valence orbital energies, gross atomic populations, and dipole moments. The results also compared favorably to previous ab initio minimum STO basis results of Lipscomb and coworkers. The 3G/MODPOT + VRDDO calculations verified that for such spatially compact molecules (such as boron hydrides, which are fragments of polyhedra), the VRDDO procedure does not result in a noticeable savings in computer time for molecules of the size and shape of B5H9 and B6H10, in contrast to the savings previously realized for organic molecules of comparable atomic size. However, the agreement in calculational results between the 3G/MODPOT and the 3G/MODPOT+VRDDO results was still as extremely close as it had been for the organic molecules.3G/MODPOT calculations were also carried out for B8H12, B9H15, B10H14, B10H14-2, 1,2-C2B4H6, and 1,6-C2B4H6 and the results compared to the previous minimum STO basis results. For B10H14, the 3G/MODPOT+VRDDO method led to savings in computer time of 28% over the 3G/MODPOT method itself.The agreement of the 3G/MODPOT results with available experimental photoelectron spectral data for B5H9 and 1,6-C2B4H6 was as good as that of the previous ab initio minimum STO basis calculations.
    Additional Material: 12 Tab.
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  • 40
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    International Journal of Quantum Chemistry 11 (1977), S. 1-15 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The influence of errors in molecular integrals on the calculated RHF energy values is considered for two models which correspond to round-off and shift errors. The energy variations induced by errors in elements of one- and two-electron matrices and the overlap matrix are represented in a quadratic approximation and the same degree of accuracy is maintained for mean values and standard deviations. The formulas given point out that mean values are less than zero when some of the errors are non-shifted. Special care is required when Gaussian lobe functions are used.
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  • 41
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    International Journal of Quantum Chemistry 11 (1977), S. 17-20 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: A derivation of most general existence conditions for surface states of a semi-infinite Kronig-Penney crystal is reported. They reduce to Steslicka's conditions under a subsidiary restriction and also indicate that the surface-state energies may lie in the allowed bulk bands. Numerical computations supporting the qualitative conclusions are provided.
    Additional Material: 2 Ill.
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  • 42
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    International Journal of Quantum Chemistry 11 (1977), S. 325-339 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: A recursive numerical integration scheme based on the method of Clenshaw and Curtis is proposed for the efficient implementation of the variation-iteration procedure for the computation of approximate energies and wave functions for atomic systems. Extensive numerical tests are carried out to assess the accuracy and efficiency of the method and inaccuracies in some earlier calculations are pointed out.
    Additional Material: 5 Tab.
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  • 43
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    International Journal of Quantum Chemistry 11 (1977), S. 359-379 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The formalism described in the first paper of this series is applied to the chain SU(2) ⊃ D′∞ ⊃ D′4 ⊃ D′2, the covering of SO(3) ⊃ D∞ ⊃ D4 ⊃ D2. The state vectors (|αJaΓγ) adapted to each link of the chain under consideration and the corresponding coupling coefficients \documentclass{article}\pagestyle{empty}\begin{document}$ f\left( {\begin{array}{*{20}c} {J_1 } & {J_2 } & J \\ {a_1 \Gamma _1 \gamma _1 } & {a_2 \Gamma _2 \gamma _2 } & {a\Gamma \gamma } \\ \end{array}} \right) $\end{document} are given in analytical form. The material reported here is very convenient for a quantum-mechanical description of molecular and nuclear systems with linear, tetragonal, or orthorhombic symmetry. In this respect, we present an outline for its applications to the electronic and vibrational-rotational spectroscopy of molecular aggregates and to the rotational spectroscopy of molecules or nuclei. In addition, we briefly show how the material may simplify the second-order non-Lie subgroup type approach to the representation theory of SU(2).
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  • 44
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    International Journal of Quantum Chemistry 11 (1977), S. 415-425 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The transferability of bonds in a set of small molecules has been explored. The molecular wave-functions have been calculated from the group (or loge) function method, via a construction based on Gaussian functions. The transferability is very good and the effect of lone pairs on adjacent bonds has been analysed. Furthermore, a very simple procedure has been proposed to estimate the frontiers of the bonds.
    Additional Material: 5 Ill.
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  • 45
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    International Journal of Quantum Chemistry 11 (1977) 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
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  • 46
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    International Journal of Quantum Chemistry 11 (1977), S. 561-576 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: It is known that the 2l+1 spherical harmonics Ylm can be transformed into cyclically equivalent orbitals, of which only a few examples have so far been given explicitly. In this article the totality of such cyclic sets is derived.It is demonstrated that other kinds of equivalent spherical harmonics do not exist.Finally a set of five equivalent d orbitals related to icosahedral symmetry is introduced.
    Additional Material: 1 Tab.
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  • 47
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    International Journal of Quantum Chemistry 12 (1977), S. 83-92 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The Hartree-Fock and first natural spin determinants were compared as reference determinants for calculating various one-electron properties such as ρ(0), 〈½∇〉, 〈r-2〉,…, 〈r3〉, and r-112〉. Calculations were made on various small atoms and their positive and negative ions. For nearly all the expectation values studied, the first natural spin orbital determinant gave consistently superior results. In particular, the Hartree-Fock functions gave markedly inferior results for some long range properties such as the magnentic susceptibilities of negative ions. The major correlation error in the expectation values is primarily an orbital effect which may be accounted for by including correlation terms in the one-particle Hamiltonian. Such approximate Brueckner or best overlap orbitals should reproduce most one-electron expectation values accurately.
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  • 48
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    International Journal of Quantum Chemistry 11 (1977) 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
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  • 49
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    International Journal of Quantum Chemistry 11 (1977), S. 399-413 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The McIver-Stanton rules concerning the symmetry of transition states have a counterpart in rules concerning the permutation symmetry of single steps in degenerate rearrangements, derivable with the aid of Longuet-Higgins group theory. The generalized rules are illustrated by the widely studied PX5 polytopal rearrangements. The analysis leads to prediction of hitherto unexplored “pseudorotation” pathways for rearrangements in ethyl and homotetrahedryl cations. CNDO computations of system energies, gradients, and curvatures at critical points on the C2H5+ and C5H5+ surfaces indicate that symmetry-breaking in keeping with the permutation-theoretic predictions is a key feature of the low-energy rearrangements of these systems. In particular, computation indicates that the C2v “classical” homotetrahedral cation corresponds to an energy maximum rather than an energy minimum, or a transition state.
    Additional Material: 5 Ill.
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  • 50
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    International Journal of Quantum Chemistry 11 (1977), S. 451-472 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Within the Schrödinger-Infeld-Hull factorization framework it is shown that, by introducing a parameter ε in the quantization condition, that is, ε(j-|m|)=integer ≥ 0, and, thus, considering “symmetrized” ladder operators, one can use the same formulas to handle both class I (ε = +1) and class II (ε = -1) problems. Starting from this unified point of view, after building up the associated angular momentum operators and their ε-dependent eigenfunctions, one unique closed-form expression of the coupling coefficients is obtained. This expression embodies many sparse and known previous results, without being more intricate than any of them. The basic material, allowing the application of a Wignera-Eckart theorem to matrix elements of an operator on the basis of eigenfunctions of factorizable equations, and a quick determination of the associated selection rules are given. Some examples are treated as an illustration.
    Additional Material: 3 Tab.
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  • 51
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: We formulated a pharmacological-physiological systems analysis and control theory based on interactive neuronal feedback loops (the effects of endogenous neurochemical diseases and exogenous psychotropic and other CNS drugs on neurotransmitter synthesis and release, reuptake, and metabolism) for normal, abnormal, and catastrophic situations.We were concerned primarily with the problems of stability or instability which might lead the system to exhibit catastrophic behavior. We set up the systems diagrams for the neurotransmitter systems and in that single framework were able to describe endogenous neurochemical disorders, the effect their drug treatment modalities had on the dynamic neurochemical balance, the effect psychotropic or other CNS drugs such as narcotics and narcotic antagonists had on neurotransmitter balance, and the interactive effect that multiple drug administration would have on neurotransmitter balance. Endogenous neurochemical disorders such as schizophrenia, Parkinsonism, depression, and mania should show up mathematically either as overly damped solutions if there is too little normal neurotransmitter or as catastrophically divergent instabilities if there is too much normal neurotransmitter. Improper mixed drug therapies, as well as the devastating effect of eating foods such as cheese (which contains sympathomimetic amines which potentiate the release of catecholamines from the presynaptic nerve endings) while on MAOI therapy also show up as mathematical, usually catastrophic, instabilities. We also indicated how this systems analysis and control theory could be put on small interactive computer terminals for use in clinical management and proper drug therapy of patients with neurochemical disorders.
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  • 52
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    International Journal of Quantum Chemistry 12 (1977), S. 593-608 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Floating spherical Gaussian orbital (FSGO) open-shell calculations have been made to determine the potential energy surface of planar square and rectangular arrangements of the four-electron system H4. This surface is discussed in relation to the bimolecular isotope exchange reaction H2+D2-→ 2HD. The changes in energy and geometry accompanying the coplanar approach of two hydrogen molecules interacting chemically have also been investigated. Calculations on the electronic energies of planar T-shaped and kite arrangements of H4 of various sizes show that it is unlikely that these configurations can serve as transition states for the exchange reaction. However, the energy curve for linear configurations of H4 (H—H—H … H), calculated as a function of the H3 … H distance with the symmetric linear H3 (H-H-H) unit fixed at the internuclear distance of 1.9080 a.u., is found to have a deep minimum (-1.9176 a.u.) at an r(H3 … H) distance of 1.5846 a.u. The overall results suggest that the following mechanism for the exchange reaction, H2+H2→H2+H+H→H3+H→H+H2+ H→H2+H2 could be advantageous as it requires a barrier height of 0.1604 a.u. which is significantly lower than that calculated from the saddle point energy (0.1950 a.u.). However, the problem of reconciling this with the experimental activation energy of 0.0685 a.u. still remains.
    Additional Material: 7 Ill.
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  • 53
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    International Journal of Quantum Chemistry 12 (1977), S. 655-670 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Excitation energies and transition moments have been determined from a second order polarization propagator and the effect of including energy shifted denominators has been investigated. Results for Be and CH+ show a change of 2-5% for the transition moments and of 0-20% for the singlet excitation energies in a second order approach compared to a first order (time-dependent Hartree-Fock) approximation. Both Be and CH+ are triplet unstable in the time-dependent Hartree-Fock approximation. The triplet instability is removed for Be but not for CH+ in a second order polarization propagator approach.
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  • 54
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    International Journal of Quantum Chemistry 11 (1977) 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
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  • 55
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    International Journal of Quantum Chemistry 11 (1977), S. 21-47 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: A full set of harmonics which are at the basis of all irreducible representations of the cubic point group and having order l ≤ 16 has been calculated in terms of Cartesian coordinates. Due to their complication, former calculations of harmonics in Cartesian coordinates for half of the irreducible representations did not exceed l = 6. The method presented in this paper is a modification of that originally given by Von der Lage and Bethe; it can be readily applied to the calculation of harmonics of arbitrary order for any irreducible representation of the cubic point group.
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  • 56
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Following Kohn (reference 4), Schlosser and Marcus (reference 3), and Weare and Parr (reference 2), an energy functional is defined for a molecular problem which is stationary in the neighborhood of the exact solution and permits the use of trial functions that are discontinuous. The functional differs from the functional of the standard Rayleigh-Ritz method in the replacement of the usual kinetic energy operators T̂(μ) with operators T̂′(μ) = T̂(μ) + Î(μ), where Î(μ) generates contributions from surfaces of nonsmooth behavior. If one uses the ∇Ψ · ∇Ψ way of writing the usual kinetic energy contributions, one must add surface integrals of the product of the average of ∇Ψ and the change of ∇Ψ across surfaces of discontinuity.
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  • 57
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    International Journal of Quantum Chemistry 11 (1977), S. 149-161 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: A method for calculating the vertical ionization potentials and electron affinities according to their fundamental definition as differences between energies of the singlet ground and doublet ionized states is developed for cyclic hydrocarbons. The method adopts a new approach based on the central idea of a recent ab initio IP and EA calculation in which orbital exponents are optimized for both ground and ionized states. Hence, all the semi-empirical parameters of the MO theory are written as functions of the effective nuclear charge which, in turn, is made self-consistent with the molecular electronic charge distribution of the species. Although the MO theory is developed in the π electron approximation, the changes in the σ electron density, resulting from the loss or gain of a π electron, are explicitly considered in the calculation. The theory is compared to the earlier work of Hoyland and Goodman and tested against the first five polyacenes and on the condensed ring aromatics phenanthrene, pyrene, and perylene. Except for perylene, the results are in close agreement with the latest photoelectron spectroscopic measurements.
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  • 58
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: A computational procedure which introduces some electron correlation into quantum mechanical calculations is described. Diverse applications are given. Among these, the method gives values of 65.6 kcal/mole for the dissociation energy of LiH, 62.0 kcal/mole for the ring-opening energy of cyclopropane, and 9.123 × 155 dynes/cm for the O-H stretching force constant of H2O. These results, and others given, suggest that our procedure has great potential and provides a very economical method for introducing electron correlation into a wave-function.
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  • 59
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    International Journal of Quantum Chemistry 11 (1977), S. 277-281 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Parseval's identity for orthonormal bases in Hilbert space is generalised to characterise uniquely biorthonormal bases among biorthonormal systems.
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  • 60
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    International Journal of Quantum Chemistry 11 (1977), S. 301-315 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: This paper studies the decay, due to the spin-lattice coupling, of two ½ spins with slightly different Zeeman energies when the lattice is thermally excited. The analysis is based on obtaining, by means of the Nakajima-Zwanzig projection operator technique, an equation for the evolution of the reduced density operator of the spin system which manifests the influence of one spin on the relaxation process of the other. The zero-order solutions obtained for the evolution of the expectation values of the spin dynamics operators are essentially equivalent to the Bloch equations; higher order solutions are also obtained.
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  • 61
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    International Journal of Quantum Chemistry 11 (1977), S. 349-358 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: A new algorithm for the computation of the density of states distributions of stereoregular polymers is presented. It is related to the Gilat-Raubenheimer technique for three dimensional systems. Its application to polyethylene is briefly described.
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  • 62
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    International Journal of Quantum Chemistry 11 (1977), S. 380-380 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
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  • 63
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    International Journal of Quantum Chemistry 11 (1977), S. 435-440 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The FSGO model has been used to make ab initio calculations of the geometry of B2H5+ ion. The results indicate that the acetylenic structure has the lowest energy (-43.881 a.u.) and the planar structure has the highest energy (-43.838 a.u.). The energy of the non-symmetric structure is only slightly higher (-43.879 a.u.) than that of the acetylenic one. Results of CNDO/2 calculations reported here also predict the acetylenic structure to be the most stable one.
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  • 64
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    International Journal of Quantum Chemistry 11 (1977), S. 524-524 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
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  • 65
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    International Journal of Quantum Chemistry 12 (1977), S. 457-469 
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The method of fractional parentage is extended to the general case of mixed configurations in arbitrary nonsimply reducible groups, G ⊂ SO(3). Particular attention is devoted to the calculation of coefficients of fractional parentage (CFP) and expressions are provided for the matrix elements of F and G type operators between N electron functions.
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  • 66
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    International Journal of Quantum Chemistry 11 (1977), S. 441-450 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: A series of LCAO-MO-SCF calculations, using various basis sets of Gaussian-type functions, has been made in order to study the effects of p, d, and f polarization functions for a 10-electron isoelectronic series of oxygen hydrides and for an 18-electron isoelectronic series of sulfur hydrides. Conclusions from these results suggest that meaningful proton affinities cannot be calculated without the inclusion of a d function on the heavy atom and a p function on the hydrogen atoms.
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  • 67
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    International Journal of Quantum Chemistry 11 (1977), S. 605-611 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The parameter optimization method of Part I is applied to the exponents of real STOS of first row atoms. In addition to minimum basis ground states, some independently optimized excited states are discussed in the case of Be. Local minima on the energy versus parameter surface are found in 4-configuration functions for the ground state of N. They are not present in either the simpler minimum basis function or in a more complete 8-configuration function.
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  • 68
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    International Journal of Quantum Chemistry 11 (1977), S. 701-701 
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
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  • 69
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    International Journal of Quantum Chemistry 11 (1977), S. 695-700 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Relativistic symmetry orbitals are given for the double group D3h. For atomic orbitals at the symmetry center a general expression is presented. The atomic orbitals of the s, p½, and p3/2 variety outside the center are also considered. The representation matrices are given in explicit form.
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  • 70
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    International Journal of Quantum Chemistry 11 (1977), S. 759-766 
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: A two-parameter ω-technique for MO calculations is proposed. The parameters ω and ω′ are chosen empirically to obtain a good agreement between calculated and observed bond lengths. The method amounts to an inclusion of the effect of nearest-neighbour electronic repulsion integrals into the conventional ω-technique.
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  • 71
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    International Journal of Quantum Chemistry 11 (1977), S. 849-867 
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: A time independent diagrammatic technique based on the Wick theorem and graphical methods of spin algebras, as outlined in Part I, is applied to a simple open shell case having one unpaired electron in addition to the pure singlet closed shell. Compact explicit expressions for the matrix elements of a spin independent Hamiltonian between conveniently chosen spin symmetry adapted states are given for the ground, mono- and bi-excited configurations.
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  • 72
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    International Journal of Quantum Chemistry 11 (1977), S. 885-894 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Gaussian orbitals are used to calculate Temple lower bounds for H2+, HeH++, and H3++. Molecular orbitals are constructed from individual Gaussian-type orbitals (GTO) and from GTO contractions adapted for either upper or lower bounds of the hydrogen atoms. The MOS are optimized by minimizing either the upper bound, 〈H〉, or the variance, 〈(H - E)2〉. The best Temple lower bounds achieved by these methods are -0.60336 a.u. for 2+, - 1.06224 a.u. for HeH++, and -0.13003 a.u. for H3++. Comparison is made with other types of molecular orbitals and with the exact wave functions for 2+, HeH++. Analysis of the nuclear cusps is given. A prescription for constructing lower bound molecular orbitals is offered.
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  • 73
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    International Journal of Quantum Chemistry 12 (1977) 
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
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  • 74
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    International Journal of Quantum Chemistry 12 (1977), S. 273-289 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The localized-site cluster expansion technique is applied to the infinite linear Heisenberg model with both nearest-neighbor and next nearest-neighbor interactions. These cluster ansätze are systematically studied and improved, up to the so-called 5-site approximation. Generally we find the present cluster ansätze yield the most accurate variational results yet available.
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  • 75
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    International Journal of Quantum Chemistry 12 (1977), S. 327-334 
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: For orbital optimization within the MC SCF theory a modification of the OEH method is proposed with the direction of descent determined according to the Fletcher-Reeves gradient method. The combined method developed on this basis ensures the convergence of the iterative process when the Hessian singularities occur. The convergence properties of the method proposed are studied by performing the ab initio water molecule calculations using two types of multiconfigurational wave functions.
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  • 76
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    International Journal of Quantum Chemistry 12 (1977), S. 369-382 
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Branching diagram and Serber-type spin functions are ordered according to their diagrams. The method of Graebenstetter et al. is slightly modified; it provides an effective algorithm for the construction of genealogical spin functions. A counterpart of the method is developed for Serber-type spin functions. Special properties of branching diagram functions and Serber-functions are established.
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  • 77
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    International Journal of Quantum Chemistry 12 (1977), S. 427-429 
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: A comparison of experimental and theoretical values for Δα = αe - αg, assuming no sigma-electron contribution, shows a great distortion by π-electron calculations. We analyze existing electrochromic data, using this assumption, and report Δα values of 44 Å3 for coronene and 43 Å3 for triphenylene. Some general properties of Δα are discussed in terms of potential energy curves which suggest interesting calculations to relate excited matrix elements with experimental measurements.
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  • 78
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    International Journal of Quantum Chemistry 12 (1977), S. 433-441 
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The energy spectrum of localized states in a simple cubic crystal is analysed, using the next-nearest neighbor approximation. The main distinguishing feature between the nearest and next-nearest neighbor approximation is the energy distribution of the localized states. Contrary to the tight-binding approximation, a non-symmetric distribution is found for clean surfaces, and split energy bands are found for surfaces completely covered by adsorbed atoms.
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  • 79
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    International Journal of Quantum Chemistry 12 (1977), S. 485-494 
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Energy bands of VO are calculated by the augmented-plane-wave and Green's function methods. The results of calculations with different potentials are compared. The physical causes for differences in the bands are discussed.
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  • 80
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    International Journal of Quantum Chemistry 12 (1977), S. 545-547 
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The two-parameter function, ϕ = (C1 + C2rn-1) exp (-ζr), (n = 2-5), has been used as a basis function to determine the independent particle model energy of two-electron atomic systems in their ground state. The best energy is found for n = 3 (He - B3+) and for n = 4 (H-). Our energy values are significantly close to Hartree-Fock results.
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  • 81
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    International Journal of Quantum Chemistry 12 (1977), S. 569-578 
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Advantages and difficulties of numerical integration in relation to a transcorrelated solution of the molecular Schrödinger equation are discussed. Because singularities in the two-electron integrals can be completely removed in a transcorrelated calculation, the major difficulty remaining to be resolved is that of singularities in the one-electron integrals. A general method of treating this problem is given which involves the derivation of some new polycentric expansion functions which are everywhere finite under the one-electron part of the Hailtonian. The important improvements obtained are illustrated by some calculations on LiH.
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  • 82
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    International Journal of Quantum Chemistry 11 (1977), S. 613-625 
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: For efficient integral evaluation, orbital basis functions are grouped into shells and integrals into blocks in the recently developed SCF program Hondo. This shell structure is ideally suited to the scheme of Dacre and Elder for using point group symmetry. An entire block of two-electron integrals is eliminated if it is symmetrically equivalent to another block with a higher index (four label). Using the “petite list” of blocks of integrals, a skeleton Fock matrix is formed from which the true Fock matrix is generated by “symmetrization.” We prove two theorems which provide a clear and rigorous justification for this version of the Dacre-Elder procedure. We compare SCF calculations on the phosphorus molecule using Td symmetry with those using various subgroups of Td. The number of integrals computed is found to be approximately inversely proportional to the order of the group. Integral evaluation time and SCF iteration time are each linear functions of the number of integrals. The computer spends a negligible amount of time in executing symmetry-related code, and the human effort involved is little more than picking the appropriate Schönflies symbol for the molecule.
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  • 83
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    International Journal of Quantum Chemistry 11 (1977) 
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
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  • 84
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    International Journal of Quantum Chemistry 11 (1977) 
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  • 85
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    International Journal of Quantum Chemistry 11 (1977), S. 895-895 
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
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  • 86
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    International Journal of Quantum Chemistry 11 (1977), S. 931-941 
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: One of the variants of Löwdin's partitioning technique that makes use of a Brillouin-type perturbation expansion for the study of lower bounds to the eigenvalues of a Hamiltonian has not been applied to any practical quantum mechanical problem so far. To illustrate how powerful this method can be, an application is made to the rigid rotator in an electric field, which has already been studied by Choi and Smith using the bracketing function of an intermediate Hamiltonian. It turns out that for a given order of the basis set of the Bazley space the Brillouin-Löwdin perturbation expansion gives closer bounds than the method of Choi and Smith, except for the case l = m, where the procedures can be shown to be mathematically equivalent. Especially for high l - m the number of basis functions needed to attain the same accuracy is by far larger for the method of Choi and Smith than for the Brillouin-Löwdin method.
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  • 87
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    International Journal of Quantum Chemistry 11 (1977), S. 991-1000 
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The solution of the quantum-mechanical one-particle problem involving a Coulomb potential with a cut-off contains Whittaker functions, difficult to evaluate individually. However, the energy expression involves a ratio of two contiguous Whittaker functions, and the entire ratio is easily expressed as a convergent continued fraction. Representative energy eigenvalues are calculated, correcting the errors due to an earlier Bessel function approximation by Wannier.
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  • 88
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    International Journal of Quantum Chemistry 11 (1977), S. 1021-1033 
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: We describe an attempt to use the AMO method for the investigation of insulator metal transitions. One of the main features of the calculation is that it permits an extension of the AMO method to finite temperatures.The ability of the model to account for such transitions is emphasized for the special case of linear antiferromagnetic systems. We discuss possible generalizations by pointing out that there exists a connection with Peierls' model.
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  • 89
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    International Journal of Quantum Chemistry 11 (1977), S. 1045-1045 
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
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  • 90
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    International Journal of Quantum Chemistry 12 (1977), S. 19-28 
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The theory for treating exchange interactions between atoms or molecules as a perturbation, which was first propoed by Jansen, is extended to general cases by the use of the group algebraic technique and a nonorthogonal basis set. As a result, a new expresion for the perturbation ket and energy of each order is obtained. A comparion of the expression with those presented by other investigators is made.
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  • 91
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    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Exact separated atom nuclei and centre of nuclear charge centred partial wave solutions for the Schrödinger equation are obtained for the 1sσ, 2sσ, 3sσ, 2pσ, 3dσ, and 3pσ states of HeH++ as a function of the internuclear separation R and the number of partial waves used to represent the wave functions for the molecules. If the expansion centre is chosen appropriately one-centre techniques are in general very efficient for these Coulomb dominated interactions relative to molecules like H+2(1sσg) which have a large electron exchange contribution to their interaction energy. In general the centre of nuclear charge is not the most suitable expansion centre for heteronuclear molecules for most values of R.
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  • 92
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    International Journal of Quantum Chemistry 12 (1977), S. 963-965 
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Additional Material: 1 Tab.
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  • 93
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    International Journal of Quantum Chemistry 12 (1977), S. 215-223 
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The invariance question int he CNDO and INDO levels of approximation is discussed with particular reference to one-center and two-center two-electron integrals and rotation of molecule-fixed coordinate axes. It is shown that asufficient condition for rotational invariance for the cone-center two-electron integrals is Jμμ = Jμμ, +2Kμμ, where J and K are the Coulomb and exchange integrals over orbitals μ μ′ with the same azimuthal quantum number. CNDO and INDO procedures, which explicitly employ Löwdin's orthogonalized basis set of atomic ortbitals (OAO) and differentiate between s-, p-, and d-orbitals on an atom in calculating various integrals, have also been examined in relation to the rotational invariance requirement. An expression which satisfies rotational invariance for two-electron Coulomb repulsion integrals over OAOS is also given.
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  • 94
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    International Journal of Quantum Chemistry 11 (1977), S. 525-542 
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Exact solutions to the quantum mechanical problem of an anisotropic oscillator in a one-dimensional magnetic field are obtained. These solutions (eigenenergies and wave functions) are then applied to the problem of calculating the magneto-optical properties of a charged spinless particle constrained to move in a harmonic potential field. General expressions for the dipole strengths and rotational strengths associated with radiation induced transitions between the eigenstates of this model system are developed, and these quantities are further related to observables of magneto-optical absorption spectroscopy and Faraday effect studies.
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  • 95
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    International Journal of Quantum Chemistry 11 (1977), S. 591-604 
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: This paper is concerned with a new application of projected-unrestricted Hartree-Fock theory, namely, the calculation of electronic spectra for symmetric molecules. The excited electronic state is represented by a single determinant whose unrestricted nature allows for orbital rearrangement relative to the self-consistent ground state. The self-consistent calculation must be followed by spin projection to obtain appropriate spin eigenstates. It was necessary to develop modified procedures for portions of the spin projection calculation because our method of constructing the wave functions produces degeneracies among the natural orbitals. Illustrative calculations using the all-valence-electron INDO approximations produced results which compared favorably with configuration-interaction treatments. The method described here should be most useful, however, in conjunction with ab initio calculations using flexible basis sets.
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  • 96
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    International Journal of Quantum Chemistry 11 (1977), S. 685-694 
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: It is shown that a substantial energy improvement is gained by the variational use of Hulthén orbitals, instead of single Slater orbitals, in the 3d shells of some excited configurations of sulphur and phosphorus. The energies obtained are close to those attained with two-term Slater functions. In some cases the radial distribution functions from Hulthén orbitals are as good an approximation of SCF radial distributions as those from two-term Slater orbitals. Single term 2d functions with only one parameter are found to give almost identical energies and radial distribution functions as those obtained from two-parameter Hulthén orbitals. It is shown that the relationship between one-term 2d orbitals and Hulthén orbitals gives a method of enforcing nuclear cusp conditions on the former with little effect on the energy.
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  • 97
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    International Journal of Quantum Chemistry 12 (1977), S. 784-784 
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
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  • 98
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    International Journal of Quantum Chemistry 12 (1977), S. 795-803 
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Strong delocalized π-bonds must be approximated by localized π-bonds within the PCILO framework. From this approximation some difficulties result in the calculation of intermolecular interactions. If only one subsystem involves delocalized π-bonds the difficulties seem to be not very important. But if both subsystems involve such bonds, the PCILO results are not reasonable in some cases.
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  • 99
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    International Journal of Quantum Chemistry 12 (1977), S. 827-839 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: A new method for the numerical calculation of (inverse) square roots of real symmetric matrices is proposed. Simplicity of the algorithm, good numerical accuracy, short computational time and the possibility to solve the problem in an (n, n) array are some of its features; in addition a new theoretical view on this problem is presented.
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  • 100
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 12 (1977), S. 875-896 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: A very general realization of the so(2, 1) algebra, which easily follows from the basic commutation relations that are satisfied by any pair of mutually conjugate generalized coordinates and momenta, is constructed. Using special cases of this general realization, and closely following the well known derivation of the eigenvalue spectra of the angular-momentum operators, based on the so(3) algebra, we derive the energy spectrum for the N-dimensional isotropic harmonic oscillator, and for both the nonrelativistic and the relativistic N-dimensional hydrogen atom. Special attention is given to a simple derivation of the form of these Hamiltonians in terms of the so(2, 1) algebra generators. In particular, the usually exploited tilting transformation is avoided, and the whole derivation is presented in an extremely simple and straightforward way. The present approach stresses the similarity and mutual relationship between the systems studied and, in addition to introducing some novel techniques and providing considerable insight into the overall structure of these problems, also has a definite pedagogical value.
    Type of Medium: Electronic Resource
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